一类多元三角多项式算子同时逼近的正逆定理

Direct and Inverse Theorems of Simultaneous Approximation for A Kind of Multivariate Trigonometric Polynomial Operators

利用光滑模和K-泛函给出了一类多元三角多项式算子同时逼近的正逆定理.进一步得出了该类算子的本质同时逼近精度和最大同时逼近能力,刻画了同时逼近精度与被逼近函数光滑性之间的关系.

Using the modulus of smoothness and K-functional, direct and inverse theorems of simultaneous approximation for a kind of multivariate trigonometric polynomial operators are established. Its accuracy and maximal ability of simultaneous approximation is obtained, and the relation between accuracy and the smoothness of function to be approximated is depicted.